Question

Pointwise convergence

Answer 1

Have can I show this
\[f_n(x)=n(x^{2/n}-1)\]
converges pointwise against \[f(x)=\ln(x)^2\]

Answer 2

Just downright take the limit? :D
\[\Large \lim_{n\rightarrow \infty}\frac{x^{\frac2n}-1}{\frac1n}\]

Answer 3

for
\[0<x<1\]
\[\lim_{n \to \infty}n(x^{2/n}-1)=0\]
so
\[\sup_{0<x<1}\left| f_n(x)-f(x) \right|=\sup_{0<x<1}\left| n(x^{2/n}-1)-0 \right|\]